# Matrix problem help. solve the remaining equation and find the value(s) for x

• flatty

| x 0 c|
| -1 x b| = 0
| 0 -1 a|

## The Attempt at a Solution

As best as I can tell I would end up with x * (xa - (-1b)) and -1c and then I would end up with Ax^2 + BX + C which leaves me confused am I looking at a quadratic equation for the answer or is there a way to get numerical values out of it?

| x 0 c|
| -1 x b| = 0
| 0 -1 a|

## The Attempt at a Solution

As best as I can tell I would end up with x * (xa - (-1b)) and -1c and then I would end up with Ax^2 + BX + C which leaves me confused am I looking at a quadratic equation for the answer or is there a way to get numerical values out of it?
Your problem statement says that the determinant of your matrix is zero.

What equation represents this?

I presume you are taking the determinant and setting it equal to zero. If so, what you've done looks right. Remember the solution to a quadratic equation? Also, you can only get a numerical answer if you know the values of a,b,c. Otherwise, the answer will be an expression involving a,b,c.

0=x*(xa-(-1b))-(-1*c)

I am using det(a)=A11(A22*A33-A23*A32)-A12(A21*A33-A23*A31)+A13(A21*A32-A22*A31)

Yes it is equal to zero sorry, new here.

Ax^2+bx+c=0 so I am assuming my answer would be x = [-b ± √(b^2 - 4ac) ]/2a

Yes, that's right.

thanks